Given that a<span>
gas station operates two pumps, each of which can pump up to 10,000
gallons of gas in a month and that the total of gas pumped at the station in a
month is a random variable y (measured in 10,000 gallons) with a
probability density function (p.d.f.) given by
Part A:
The value of c that makes f(y) a pdf is obtained as follows:
![F(\infty)= \int\limits^{\infty}_{-\infty} {f(y)} \, dy=1 \\ \\ \Rightarrow \int\limits^1_0 {cy} \, dy +\int\limits^2_1 {(2-y)} \, dy=1 \\ \\ \Rightarrow \left. \frac{cy^2}{2} \right]^1_0+\left[2y- \frac{y^2}{2} \right]^2_1=1 \\ \\ \Rightarrow \frac{c}{2} +4-2-2+ \frac{1}{2} =1 \\ \\ \Rightarrow \frac{c}{2} = \frac{1}{2} \\ \\ \Rightarrow \bold{c=1}](https://tex.z-dn.net/?f=F%28%5Cinfty%29%3D%20%5Cint%5Climits%5E%7B%5Cinfty%7D_%7B-%5Cinfty%7D%20%7Bf%28y%29%7D%20%5C%2C%20dy%3D1%20%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20%5Cint%5Climits%5E1_0%20%7Bcy%7D%20%5C%2C%20dy%20%2B%5Cint%5Climits%5E2_1%20%7B%282-y%29%7D%20%5C%2C%20dy%3D1%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20%5Cleft.%20%5Cfrac%7Bcy%5E2%7D%7B2%7D%20%5Cright%5D%5E1_0%2B%5Cleft%5B2y-%20%5Cfrac%7By%5E2%7D%7B2%7D%20%5Cright%5D%5E2_1%3D1%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20%20%5Cfrac%7Bc%7D%7B2%7D%20%2B4-2-2%2B%20%5Cfrac%7B1%7D%7B2%7D%20%3D1%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20%5Cfrac%7Bc%7D%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20%5Cbold%7Bc%3D1%7D%20)
Part B:
We compute E(y) as follows:
![E(y)=\int\limits^{\infty}_{-\infty} {yf(y)} \, dy \\ \\ =\int\limits^1_0 {y^2} \, dy +\int\limits^2_1 {(2y-y^2)} \, dy \\ \\ =\left. \frac{y^3}{3} \right]^1_0+\left[y^2- \frac{y^3}{3} \right]^2_1 \\ \\ = \frac{1}{3} +4- \frac{8}{3} -1+ \frac{1}{3} \\ \\ =1](https://tex.z-dn.net/?f=E%28y%29%3D%5Cint%5Climits%5E%7B%5Cinfty%7D_%7B-%5Cinfty%7D%20%7Byf%28y%29%7D%20%5C%2C%20dy%20%5C%5C%20%20%5C%5C%20%3D%5Cint%5Climits%5E1_0%20%7By%5E2%7D%20%5C%2C%20dy%20%2B%5Cint%5Climits%5E2_1%20%7B%282y-y%5E2%29%7D%20%5C%2C%20dy%20%5C%5C%20%20%5C%5C%20%3D%5Cleft.%20%5Cfrac%7By%5E3%7D%7B3%7D%20%5Cright%5D%5E1_0%2B%5Cleft%5By%5E2-%20%5Cfrac%7By%5E3%7D%7B3%7D%20%5Cright%5D%5E2_1%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2B4-%20%5Cfrac%7B8%7D%7B3%7D%20-1%2B%20%5Cfrac%7B1%7D%7B3%7D%20%20%5C%5C%20%20%5C%5C%20%3D1)
Therefore, E(y) = 1.
</span>
Answer:
20
Step-by-step explanation:
Remember PEMDAS!
So first parentheses:
1.6^2 = 2.56
8.7 + 9.3 = 18.
Because that is inside another parentheses you multipy them.
2.56 x 18 = 46.08
Now: 46.08 divided by 1.8 = 25.6
Now subtract:
25.6 - 3.7 - 1.9 which equals 20!
Hope that helped!
Answer:
You can not divide by zero.
The inequality is equivalent to - 20.2 > 0 which is false.
Step-by-step explanation:
We can not divide both sides by zero, because if we divide both sides by zero, then the inequality becomes
⇒ - ∞ > y, which is not possible.
Again, the given inequality is - 20.2 > 0 × y.
We have to multiply y with zero and a product of zero with any term is also zero.
Hence, the inequality becomes - 20.2 > 0.
Therefore, the inequality is equivalent to - 20.2 > 0 which is false. (Answer)
Answer:
There is not sufficient evidence to support the claim.
Step-by-step explanation:
The claim to be tested is:
The mean respiration rate (in breaths per minute) of students in a large statistics class is less than 32.
To test this claim the hypothesis can be defined as follows:
<em>H₀</em>: The mean respiration rate of students is 32, i.e. <em>μ</em> = 32.
<em>Hₐ</em>: The mean respiration rate of students is less than 32, i.e. <em>μ</em> < 32.
The sample mean respiration rate of students is 31.3.
According to the claim the sample mean is less than 32.
The sample mean value is not unusual if the claim is true, and the sample mean value is also not unusual if the claim is false.
Thus, there is not sufficient evidence to support the claim.
1. "the graph has the same zeros" : so let a be the "triple" root of the cubic polynomial function.
2. So f(x)=
3. Don't forget that the expression might have a coefficient b as well, and still maintain the conditions:
4. Now, f(0)=-5 so
5. the function is
where a can be any real number except 0
